Adaptation to local values of field variables can be achieved by placing grid nodes on constant value contours. The points also need to be distributed on each contour, based on local gradient. This ensures a distribution of grid nodes that is well-adapted to local gradients. An implementation procedure has been developed to achieve the adaptation algorithm. Methods for boundary adaptation and grid smoothing is also included. The effects of different parts of the algorithm on the final solution is demonstrated by implementing features in sequence. The test case is transient conduction in singly and multiply connected domains. Computation time reduction of a factor of five compared to equivalent accuracy constant grid solution has been achieved. The number of nodes is reduced by as much as a factor of seven.